This is a text for a one-quarter or one-semester course in probability, aimed at students who have done a year of calculus. The book is organised so a student can learn the fundamental ideas of probability from the first three chapters without reliance on calculus. Later chapters develop these ideas further using calculus tools. The book contains more than the usual number of examples worked out in detail. The most valuable thing for students to learn from a course like this is how to pick up a probability problem in a new setting and relate it to the standard body of theory. The more they see this happen in class, and the more they do it themselves in exercises, the better. The style of the text is deliberately informal. My experience is that students learn more from intuitive explanations, diagrams, and examples than they do from theorems and proofs. So the emphasis is on problem solving rather than theory.

Autorentext

Jim Pitman is a Professor in the Departments of Statistics and Mathematics in the University of California at Berkeley, USA.

Inhalt

1 Introduction.- 1.1 Equally Likely Outcomes.- 1.2 Interpretations.- 1.3 Distributions.- 1.4 Conditional Probability and Independence.- 1.5 Bayes' Rule.- 1.6 Sequences of Events.- Summary.- Review Exercises.- 2 Repeated Trials and Sampling.- 2.1 The Binomial Distribution.- 2.2 Normal Approximation: Method.- 2.3 Normal Approximation: Derivation (Optional).- 2.4 Poisson Approximation.- 2.5 Random Sampling.- Summary.- Review Exercises.- 3 Random Variables.- 3.1 Introduction.- 3.2 Expectation.- 3.3 Standard Deviation and Normal Approximation.- 3.4 Discrete Distributions.- 3.5 The Poisson Distribution.- 3.6 Symmetry (Optional).- Summary.- Review Exercises.- 4 Continuous Distributions.- 4.1 Probability Densities.- 4.2 Exponential and Gamma Distributions.- 4.3 Hazard Rates (Optional).- 4.4 Change of Variable.- 4.5 Cumulative Distribution Functions.- 4.6 Order Statistics (Optional).- Summary.- Review Exercises.- 5 Continuous Joint Distributions.- 5.1 Uniform Distributions.- 5.2 Densities.- 5.3 Independent Normal Variables.- 5.4 Operations (Optional).- Summary.- Review Exercises.- 6 Dependence.- 6.1 Conditional Distributions: Discrete Case.- 6.2 Conditional Expectation: Discrete Case.- 6.3 Conditioning: Density Case.- 6.4 Covariance and Correlation.- 6.5 Bivariate Normal.- Summary.- Review Exercises.- Distribution Summaries.- Discrete.- Continuous.- Beta.- Binomial.- Exponential.- Gamma.- Geometric and Negative Binomial.- Hypergeometrie.- Normal.- Poisson.- Uniform.- Examinations.- Solutions to Examinations.- Appendices.- 1 Counting.- 2 Sums.- 3 Calculus.- 4 Exponents and Logarithms.- 5 Normal Table.- Brief Solutions to Odd-Numbered Exercises.